List of top General Aptitude Questions asked in GATE PI

In the given figure, $\overline{PQ}$ is the diameter of a circle with center $O$. Two points $R$ and $S$ are chosen on the circle such that $\angle ROS = 80^\circ$. When $\overline{PR}$ and $\overline{QS}$ are extended, they meet at $T$.

The value of $\angle RTS$ is ______

Based on the relationship between each polygon and the number inside it, the value of 'X' is ______

Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF state. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules:
Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON.
Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
The state of any bulb not meeting the conditions above is left unchanged.
The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.

The number of bulbs which are ON at the end of Step 8 is ______

$P$ and $Q$ are two positive integers such that $P^2 = Q^2 + 13$.
The product of the numbers $P$ and $Q$ is ______

The figure below is supposed to show three non-overlapping shapes, one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated by '?' and completes the oval and the two triangles?

Match the words in Column I with their synonyms in Column II.

Column I	Column II
(i) Lonely	(p) Verbatim
(ii) Literal	(q) Solitary
(iii) Lousy	(r) Deadly
(iv) Lethal	(s) Terrible

At how many points will the curves $ y = x^2 $ and $ y = -x^2 - 2x - 1 $ intersect in the real $ (x, y) $ plane?

Which one of the following figures P, Q, R, or S, correctly shows the $ 45^\circ $ clockwise-rotated version of figure (I)?

'If Anish had scored hundred runs in today's match, he would have been made the captain of his team. He would have then become the youngest captain in his team's history. Unfortunately, he got out without scoring any runs. Hence, there won't be any change in the captaincy for now.'
Based on the paragraph above, which one of the following statements is true?

'The shopkeeper sells lemons.'
In this sentence, the word 'lemons' is the ________.

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of $ P $, $ Q $, and $ R $?

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius $ r $ cm as shown in the figure. The side of the dodecagon is $ d $ cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side $ r $ cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:

Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk.

A rectangle has a length $L$ and a width $W$, where $L>W$. If the width, $W$, is increased by 10%, which one of the following statements is correct for all values of $L$ and $W$?
Select the most appropriate option to complete the above sentence.

A 4 × 4 digital image has pixel intensities (U) as shown in the figure. The number of pixels with $ U \leq 4 $ is:

We __________ tennis in the lawn when it suddenly started to rain.
Select the most appropriate option to complete the above sentence.

Given matrices \[ A = \begin{bmatrix} 1 & -1 & 4 \\ 3 & 2 & -1 \\ 2 & 1 & -1 \end{bmatrix} \quad\text{and}\quad B = \begin{bmatrix} B_{11} & B_{12} & B_{13} \\ B_{21} & B_{22} & B_{23} \\ B_{31} & B_{32} & B_{33} \end{bmatrix} \] $B$ is skew-symmetric matrix of $A$. $B_{13}$ is?

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

In the given figure, PQRS is a parallelogram with $PS = 7~\text{cm}$, $PT = 4~\text{cm}$ and $PV = 5~\text{cm}$. What is the length of $RS$ in cm? (The diagram is representative.)

Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

The non-linear differential equation from the following options is

The power series expansion of a function is given as \[ \frac{1}{x}\ln(1 + x) = 1 + bx + cx^2 + ..... \] for $0<x \leq 1$. The values of constants $b$ and $c$, respectively, are

The coefficient of $x^4$ in the polynomial $(x - 1)^3(x - 2)^3$ is equal to .......................

In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics. When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college. Based only on the above information, which one of the following statements can be logically inferred with certainty?

Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty? (i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.